Oleg is training for a triathlon. One day, he jogged for 2 hours at x miles per hour. Then he bicycled for 2 hours at y miles per hour. Finally, he swam a distance of 2 miles. The total number of miles did not exceed 30 miles.
What is the greatest possible speed that Oleg could have bicycled that day?

Answer:

Correct, the inequality y ≥ 0.8x + 1.5 accurately describes the relation between the duration of the hike (x) and the amount of water needed (y). This inequality means that for any duration of the hike (x), the amount of water needed (y) must be greater than or equal to 0.8x + 1.5.

Note that the line of Best fit is attached accordingly. See the definition below.

A line of best fit is a straight line that represents the trend of a set of data.

It is used to summarize and analyze the relationship between two variables in a scatter plot. Note that the line of best fit can be used to approximate the trend or pattern of the data and make predictions for new observations that fall within the range of the data.

The line is drawn in a way that minimizes the distance between the observed data points and the line.

The line of best fit can be used to make predictions and identify outliers. It is important because it helps to reveal patterns and trends in data and allows us to make informed decisions based on the information.

Note that the line takes a position that gives an approximately equal amount of variables or data points on either side.

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18,995 × 0.82^(6) = $5,774 so he should not sell

if the percentage decrease is 18% then do 100% - 18% which is 82. divide by 100 = 0.82. if it does this for 6 years then do 18,995 × 0.82^(6) because it's 6 years. the number is larger than Manuel's offer therefore he shouldnt sell

Options A and C are correct for the condition 5 x 4 = 20.

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Factors can be found using either division or multiplication. Rules of divisibility can also be applied.

Given 5 x 4 = 20

factors of 20 are 2*2*5

so 5 is the factor of  20,

A is correct.

now multiples of 20 are 20, 40, 60.......

since all values are greater than 5,

so 5 is not a multiple of 20.

B is not correct.

now multiples of 4 are 4, 8, 12, 16, 20, 24 .......

so 20 is a multiple of 4,

C is correct.

Hence A and C are correct statements.

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Answer:

2/ c, e

Step-by-step explanation:

A graph can only be a function if one x only has one y.

If you use the line test, you see that only graphs C and E pass the test.

So, the answers are C and E.

Answer:

Step-byoooooooooooo

-step explanation:

Answer:

The value of x =10

Step-by-step explanation:

2x+ 5 = 25

Subtract 5 from each side.

2x+5-5 = 25-5

2x = 20

Divide each side by 2.

2x/2 = 20/2

x =10

The value of x =10.

Answer:

10

Step-by-step explanation:

Move the 5 to the right so the equation is 2x = 25 - 5
Then its 2x = 20 and 20/2 is 10.

It depends on the length of the festival, the length of each band's performance, and other factors. There could be any number of ways to schedule their appearances.

The number of ways to schedule the bands' appearances at the weekend festival depends on a variety of factors such as the length of the festival, the length of each individual band's performance, and the number and type of stages available.

For example, if the festival runs for two days and each band's performance is one hour, there could be a total of 22 hours of music, so eleven bands could each perform twice, once on each day.

Alternatively, if the festival has three stages and two of the stages are dedicated to different genres of music, then the bands could be scheduled to perform on those stages, with each stage hosting five bands each day.

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Answer:

Step-by-step explanation:

Let [tex]f(x) = y[/tex]

∴ [tex]y = \sqrt[3]{x + 2} -5[/tex]

x has to be isolated and made the subject of the formula:

[tex]y + 5 = \sqrt[3]{x + 2}[/tex]

Cube is applied to both sides of the equation to get rid of the cube root:

[tex](y + 5)^{3} = x + 2[/tex]

x = [tex](y + 5)^{3} -2[/tex]

Substitute [tex]f^{-1} (y) = x[/tex]:

[tex]f^{-1} (y) = (y + 5)^{3} - 2[/tex]

Replace y  with x:

[tex]f^{-1} (x) = (x + 5)^{3} -2[/tex]

The reduction of the fraction is (y-3)/4.

Suppose the fraction is proper (the numerator is smaller than the denominator).

Let it be [tex]\dfrac{a}{b}[/tex]

Then, we can interpret it as:

[tex]\dfrac{a}{b}[/tex]= a parts out of b parts of a thing.

There is a fraction, containing numerator(upper value) and denominator(lower value).

When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction.

A proper fraction is also called fraction which is less than 1.

And an improper fraction is ≥ 1

A mixed fraction contains a sum of whole number and a proper fraction.

Given;

=y^2-9/4y+12

=y^2-3^2/4(y+3)

=(y+3)(y-3)/4(y+3)

=y-3/4

Therefor, the answer of fraction will be (y-3)/4

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The equations are H = 4x + 60 and P = 8x + 20. We need to rent 10 tables to ensure that the cost of the rental will be the same.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

Let us suppose tables as x.

Given that,

The happy party rents tables for $4 per table plus a delivery fee of 60. This is expressed as:

H = 4x + 60

Party Rental rents tables for $8 per table plus a $20 delivery fee.

P = 8x + 20

To get the same cost of the rent:

H = P

4x + 60 = 8x + 20

60 - 20 = 8x - 4x

40 = 4x

x = 10

Hence, we need to rent 10 tables to ensure that the cost of the rental will be the same.

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We may determine that the values of x and y are -2 and -8, respectively, by replacing the linear equations.

A linear equation is a first-order (linear) term and a constant in an algebraic equation of the type y=mx+b, where m is the slope and b is the y-intercept.

The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."

The typical form for linear equations with two variables is Ax+By=C.

For instance, the linear equation 2x+3y=5 is in standard form.

Finding both intercepts of an equation in this style is quite easy (x and y).

The following is the equation:

y=4x ...(1)

x+y=-10 ...(2)

Now change equation (2) to y = 4x:

x+y=-10

x+4x=-10

5x = -10

x = -10/5

x = -2

Then, change equation (1) to read x = -2:

y = 4x

y = 4(-2)

y = -8

Therefore, we may determine that the values of x and y are -2 and -8, respectively, by replacing the linear equations.

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Answer:

60%

Step-by-step explanation:

12/20 = 0.6  multiply this by 100% = 60%

Answer:

  g(x) = -1/4x²

Step-by-step explanation:

Given f(x) = x² and point (2, -1) on the graph of g(x), which is a scaled version of f(x), you want the equation for g(x).

The scale factor k will satisfy ...

  g(x) = k·f(x)

  g(2) = k·f(2) . . . . . . true at the given point

  -1 = k·2² = 4k . . . . use the coordinates of the given point

  k = -1/4 . . . . . . . . . divide by 4

The equation of g(x) is ...

  g(x) = -1/4x²

Answer:

To enlarge a triangle by a scale factor of 1/2 with the center (2, 0), each vertex of the triangle should be multiplied by 1/2 and then shifted so that the center of the new triangle is (2, 0).

Step-by-step explanation:

For example, if the original triangle has vertices at (a, b), (c, d), and (e, f), the vertices of the new triangle would be at ((a-2)/2 + 2, (b-0)/2 + 0), ((c-2)/2 + 2, (d-0)/2 + 0), and ((e-2)/2 + 2, (f-0)/2 + 0).

The total number of possible outcomes is the product of the number of outcomes for each event.

The spinner can land on any of its 5 sections on the first spin, and on any of the 5 sections again on the second spin. So there are 5 x 5 = 25 possible outcomes for the spinner.

The dice can land on any of its 6 sides.

The coin can land either heads or tails.

Therefore, the total number of possible outcomes is:

25 (spinner) x 6 (dice) x 2 (coin) = 300 possible outcomes.

Answer:

p = 150 - 65

Step-by-step explanation:

We know

p is the amount he has left to raise

The target is $150

He has $65

So, the equation is

p = 150 - 65

When computing the area of a circle, the mathematical constant pi () is required. Pi is the circumference-to-diameter ratio of a circle and is approximately equal to 3.14159.

The area of a circle is calculated by multiplying pi by the radius squared (r2). To estimate the area of a circle, utilize pi in the calculation since it is a vital aspect of the relationship between the circumference and diameter of a circle.

Pi is not required when determining the area of a square, rectangle, or cube since the formulas for these shapes are different.

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The question is -

The mathematical constant pi is needed when calculating the area of a _.

a. circle

b. square

c. rectangle

d. cube

Dragging each description to explain each part of Hasan's and Bella's expressions is as follows:

d = Original price of book

0.25 = Percent Discount

0.25d = Amount of Discount

d - 0.25d = Sale price of book

0.75 = Percent of original price Bella will pay

d = original price

0.75d = Sale price of book

An algebraic expression is a combination of variables, constants, numbers, and values using the mathematical operands, including addition (+), subtraction (-), division (÷), and multiplication (×).

An algebraic expression does not have the equal symbol (=) unlike an equation.

Thus, the correct descriptions has been dragged to each part of both Hasan's and Bella's expressions.

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Step-by-step explanation:

Let s = the amount of flour in a batch of shortbread, let c = the amount of flour in a batch of croissants, and let p = the amount of flour in a pound cake.

The first statement can be written as 5s + 4p + 2c = 3525.

The second statement can be written as s + c + p = 1020.

The third statement can be written as 4p = 2c.

Multiplying the third equation by 2, we get 8p = 4c.

Subtracting this from the first equation, we get 5s + 4p + 2c - 8p = 3525 - 8p.

Simplifying, we get 5s - 6c = 3525 - 8p.

Now we have a system of two equations with the variables c and p:

5s - 6c = 3525 - 8p

s + c + p = 1020

We can use substitution to eliminate c. Solving the second equation for c, we get c = 1020 - s - p.

Substituting this into the first equation, we get 5s - 6(1020 - s - p) = 3525 - 8p.

Expanding the second equation and simplifying, we get 11s = 4545 - 8p.

Solving for s, we get s = (4545 - 8p) / 11.

Substituting the value of s into the second equation, we get c + p + (4545 - 8p) / 11 = 1020.

Expanding and simplifying, we get c + p + (4545 - 8p) / 11 = 1020.

Expanding, we get c + p = 1020 - (4545 - 8p) / 11.

Solving for c and p, we find that c = 664 grams and p = 356 grams.

Finally, the value of s is (4545 - 8 * 356) / 11 = 735 grams.

Answer:

[tex]y = -2x + 10[/tex]

Step-by-step explanation:

The slope-intercept form of equation of line:

y = mx + c

where:

m = slope

c = y-intercept

Slope, m:   [tex]\frac{y_{2} - y_{1}}{x_{2} -x_{1}}[/tex]

               = [tex]\frac{4 - 8}{3 - 1}[/tex]

               = [tex]-\frac{4}{2}[/tex]

               = [tex]-2[/tex]

[tex]y = -2x +c[/tex]

Substitute the coordinates of either of the two points in this equation to calculate the value of c:

8 = [tex]-2[/tex](1) + c

8 = [tex]-2[/tex] + c

c = 8 + 2

c = 10

Therefore, the equation is:

[tex]y = -2x +10[/tex]

The best prediction that the coin would land on heads wold be 6

If you flip a fair coin 12 times, the best prediction for the number of times it will land on heads is 6. This is because each flip has an equal chance of landing on heads or tails, and if you flip a fair coin 12 times, the expected number of heads is 6. This is because each flip has a 50% chance of landing on heads.

In the coin, there are going to be 6 changes foe head and also 6 chains for tails. This is a 50 50 chance

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Answer: An isosceles triangle is a triangle with two sides that are congruent (equal in length). If DEF is isosceles with base DF, then DE and EF are congruent and have the same length. This means that the two sides of the triangle are equal in length, and that the angle formed by DE and EF is equal to each other (since they are congruent sides, they must also be congruent angles). The two equal angles are called the base angles of the isosceles triangle.

Step-by-step explanation:

The relationship between the radius and volume of a cylinder with a height of 4 feet is nonlinear because the volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. In this case, the height is fixed at 4 feet. As we change the radius, the volume changes in a nonlinear manner.

The volume increases much faster as the radius increases. This can be seen from the exponential nature of the formula, as the radius is squared. Therefore, even a small increase in the radius results in a substantial increase in the volume, making the relationship between radius and volume nonlinear.

In contrast, if the height were to be proportional to the radius, then the relationship between radius and volume would be linear. This is because the volume would be proportional to the product of the radius and height, which is a linear relationship.

Therefore, the nonlinear relationship between radius and volume, in this case, is due to the exponential nature of the formula for the volume of a cylinder and the fixed height of 4 feet.

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--The given question is incomplete; the complete question is

"This function represents the relationship between the radius of cylinders with a height of 4 feet and their volumes. Why is this relationship between radius and volume nonlinear?"--

The limit of the function in this problem is given as follows:

lim x->0 f(x) = 1/2.

Following the standard procedure to obtain the limit of the function, merely obtaining the numeric value at x = 1, the limit is undetermined at x = 0, as follows:

0/0.

Hence the can apply the L'Hospital Rule, trying to find the derivative at the numerator and the denominator, hence:

At x = 0, the limit would again assume an undetermined value of 0/0, hence the L'Hospital Rule is applied again, hence:

Now the function is:

f(x) = cos(2x)sqrt(cos(2x))/2.

Since cos(x) = 0, the numeric value at x = 0 is given as follows:

f(0) = 1/2.

Which is the limit.

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Step-by-step explanation:

We have the point (-8, 7)

When we reflect across the X-AXIS, then the Y coordinate changes signs

When we reflect across the Y-AXIS, then the X coordinate changes signs

So when we reflect (-8, 7) across the x-axis, it becomes (-8, -7) since we change signs for the Y coordinate from +7 to -7

Reflecting across the Y, it becomes (8, 7), because we change signs from -8 to +8

On solving the provided question, we can say that Sammy has 900 fish and 200 dies and equation will be => x - y = 700

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Sammy has 900 fish and 200 dies

equation will be

x - y = 700

x = alive fishes

y = died fishes

remaining fishes are 700

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Answer:

(4, 5)

Step-by-step explanation:

Add the two x values and divide by two, add the two y values and divide by two. Then put them in brackets and those are your coordinates.

Answer:

(-3, 9)

2

Step-by-step explanation:

The command in Stata would be the most useful is reg when  you want to combine this with a dataset that reports how much each individual sleeps per week.

A collection of data is known as a data set (or dataset). In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable. The data set includes values for each of the variables, such as the object's height and weight, for each set member. Data sets may also include a group of files or documents.

For data management, visualisation, statistics, and automated reporting, Stata is a general-purpose statistical software programme created by StataCorp. Researchers in a variety of disciplines, such as science, biomedicine, epidemiology, and sociology, use it.

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